Goddard, Wayne D.; Oellermann, Ortrud R. On the cycle structure of multipartite tournaments. (English) Zbl 0840.05026 Alavi, Yousef (ed.) et al., Graph theory, combinatorics, and applications, Vol. 1. Proceedings of the sixth quadrennial international conference on the theory and applications of graphs held at Western Michigan University, Kalamazoo, Michigan, May 30-June 3, 1988. New York: John Wiley & Sons Ltd. Wiley-Interscience Publication. 525-533 (1991). Summary: It is shown that if \(T\) is a strongly connected \(n\)-partite tournament, \(n\geq 3\), then every vertex of \(T\) lies on a cycle that contains vertices from exactly \(m\) partite sets for every \(m\) with \(3\leq m\leq n\). Furthermore, \(T\) has a cycle of every length \(m\) for \(3\leq m\leq n\). Finally, every strongly connected \(n\)-partite tournament, \(n\geq 3\), contains at least \((n- 2)\) 3-cycles, and the sharpness of this result is discussed.For the entire collection see [Zbl 0831.05002]. Cited in 1 ReviewCited in 16 Documents MSC: 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles Keywords:digraph; strongly connected orientation; tournament; cycle PDFBibTeX XMLCite \textit{W. D. Goddard} and \textit{O. R. Oellermann}, in: Graph theory, combinatorics, and applications, Vol. 1. Proceedings of the sixth quadrennial international conference on the theory and applications of graphs held at Western Michigan University, Kalamazoo, Michigan, May 30-June 3, 1988. New York: John Wiley \&| Sons Ltd.. 525--533 (1991; Zbl 0840.05026)